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Quantum Reaction-Limited Reaction-Diffusion Dynamics of Noninteracting Bose Gases

This repository contains figure data and code implementation of the paper 'quantum reaction-limited reaction-diffusion dynamics of noninteracting Bose gases'.

Table of Contents
  1. Abstract
  2. Getting Started
  3. Usage
  4. License

Abstract

We investigate quantum reaction-diffusion systems in one-dimension with bosonic particles that coherently hop in a lattice, and when brought in range react dissipatively. Such reactions involve binary annihilation ($A + A \to \emptyset$) and coagulation ($A + A \to A$) of particles at distance $d$. We consider the reaction-limited regime, where dissipative reactions take place at a rate that is small compared to that of coherent hopping. In classical reaction-diffusion systems, this regime is correctly captured by the mean-field approximation. In quantum reaction-diffusion systems, for noninteracting fermionic systems, the reaction-limited regime recently attracted considerable attention because it has been shown to give universal power law decay beyond mean field for the density of particles as a function of time. Here, we address the question whether such universal behavior is present also in the case of the noninteracting Bose gas. We show that beyond mean-field density decay for bosons is possible only for reactions that allow for destructive interference of different decay channels. Furthermore, we study an absorbing-state phase transition induced by the competition between branching $A\to A+A$, decay $A\to \emptyset$ and coagulation $A+A\to A$. We find a stationary phase-diagram, where a first and a second-order transition line meet at a bicritical point which is described by tricritical directed percolation. These results show that quantum statistics significantly impact on both the stationary and the dynamical universal behavior of quantum reaction-diffusion systems.

Getting Started

The data to create figures can be found in the results folder. The code to create the figures can be found in the source-code (src) folder. There are two python scripts (phasediagram.py, qrd_dynamics.py), one containing the code used to create the phase diagram (Fig. 6 in the paper) and the other containing the code to create the dynamics and finding the effective exponent (Figs. 2-5 in the paper).

Downloading the code

A copy of the files and code can be downloaded by cloning the git repository:

git clone https://github.com/AG-Lesanovsky/2023-quantum-reaction-diffusion-dynamics-of-bose-gases

Requirements

To run the code a working Python environment is needed. The requirements the can be installed with pip:

pip install -r requirements.txt`

Usage

To run the code:

python <path-to-code-file>

License

Distributed under the CC-BY 4.0 License. See LICENSE.txt for more information.